The optimal approximation of eigenvalues and eigenfunctions from second-order elliptic spectral problems by means of Galerkin finite element methods (FEM) is well-established. We refer the reader to the seminal contributions in Vainikko [1]}, [2]}, Bramble and Osborn [3]}, Strang and Fix [4]}, Osborn [5]}, Descloux et al. [6]}, [7]}, Babuška and Osborn [8]}, and to the more recent reviews in [9]}, [10]}. The approximation of elliptic spectral problems has also been studied by means of mixed finite element methods [11]}, [12]}, [13]}, discontinuous Galerkin methods [14]}, [15]}, hybridizable discontinuous Galerkin methods [16]}, [17]}, hybrid high-order methods [18]}, [19]}, and virtual element methods [20]}. All of these methods deliver optimally convergent approximations. Since the eigenfunctions become more and more oscillatory in the upper part of the spectrum, their approximation is accurate only in the lower part of the spectrum. In contrast, isogeometric analysis [21]} delivers a more accurate approximation in the upper part of the spectrum (see also [22]}, [23]}, [24]} for some recent improvements on the subject).
